Who’s afraid of the big bad yield curve?

The yield curve plots the interest rate paid on different Treasury securities as a function of the number of years until the security matures. Usually investors require a higher yield on longer-term assets, so that the yield curve slopes up, as it did a year ago. As of a month ago, the extra yield on 10-year over 1-year bonds had all but disappeared, and this week the 10-year rate at times actually slipped below the 1-year rate, creating an inversion of the usual upward slope over at least part of the yield curve.

Why did this happen? The short rate has been rising rapidly because the Federal Reserve is concerned about inflation and has been raising rates to slow the economy. The longer term yields fell this month because investors’ expectations of both inflation and the level of economic activity likely slipped a bit, along with a possible decline in the term premium. All of these factors usually suggest the likelihood of a slowdown in economic activity.

One way this is often summarized is by looking at the spread between interest rates of two different maturities. For example, the graph on the left summarizes the implications of the spread between the 10-year Treasury and the overnight fed funds rate. Each quarter between 1959:I and 2004:II is represented by a separate diamond on this scatter diagram. The horizontal coordinates correspond to the yield on a 10-year Treasury security minus that for an overnight fed funds loan during an average day of the last month of that quarter. The vertical coordinate corresponds to the average logarithmic growth rate of real GDP over the six quarters beginning with that quarter, quoted at an annual rate. The positive correlation represents the fact that the lower the gap between 10-year yields and the fed funds rate, the slower average growth we’ve usually observed for the economy over the next year and a half. The indicated regression line summarizes this tendency– the regression coefficient of 0.6 means that for every 100 basis point decline in the spread there is on average a 60 basis point decline in average growth rates.

The first thing to emphasize about this relationship is that it’s not a sure thing. For example, in 1995:IV the spread was near its current low level of 11 basis points, and yet we saw 3.9% average growth between 1995:IV and 1997:I. In 1965:I and 1965:II the spread was 17 basis points, only a little higher than its current value, and the economy boomed at a 6-7% growth rate. Instead, the correlation summarizes an average or typical tendency– in 84% of the quarters in which we saw a spread as low as its current value or lower, subsequent growth came in slower than the historical 3.3% average.

A second point worth emphasizing (which I also discussed at length here) is that this is not something that only matters when the yield curve completely inverts or the spread becomes negative. Rather, the scatter diagram above suggests a gradual concern– the narrower the gap between long- and short-term rates, the slower growth we can usually expect to see.

With the 10-year rate currently at 4.38% and fed funds at 4.25%, the spread 0.13% is 73 basis points below its historical average of 0.86%. The regression above suggests that this would typically mean growth that is 0.44% slower than average, or under 3% annual growth for the next year and a half.

So how exactly might these concerns show up? Well, for example, Bloomberg reports today:

Sales of existing homes fell to an eight-month low in November, leaving the number of houses on the market at the highest since 1986 and suggesting one pillar of the U.S. economy will weaken next year.

18 thoughts on “Who’s afraid of the big bad yield curve?”

Thanks. R2 is not too hot, but it looks like the relationship is there graphically, although it’s loose.
So, according to the graph, as long as the spread is >0, most likely the GDP growth would be positive. Since the Fed controls the Fed Funds rate, can we conclude that every time the spread goes below zero, the Fed DELIBERATELY put the US economy on the path of recession?

I find the alarm from investment letters to be over done. The history of “close to zero” spread has ranged from positive 7.25 to negative 1.25 with a clear bias to the positive. The big question is which is going to get hit harder, inflation or nominal GNP? Should it be that inflation is lowered sharply, leaving real GNP relatively unchanged, the stock market could be off to the races.
An inverted curve is just as much a forecast of lower interest rates as a forecast of slower growth. I would love to see the same scatter gram of ten year rates 6 and 12 months later. As always, I thank you for your excellent post.

That line doesn’t look like a particularly good fit to me, especially at the left side. I think it is being constrained to burrow through the bulk of the data in the upper right, allowing it to diverge quite a bit from the data points at the left. If you sparsened out the right-hand-side data I’ll bet you’d get a very different fit.
Also, it doesn’t look like that linear a relation to me. I’d suggest you’d get a better fit with a curve concave upward. I don’t know if there is any theoretical model that would point to a suitable curve, though.
It’s surprising, with all of the panicking over the inversion, that the economy is still predicted to grow even with a negative differential. (Maybe this is because the two rates you are differencing are not as comparable as bonds of different maturity.) If the bottom line is, as you say, 0.44% lower growth than average, that is not an enormous reason for concern.

Dr. Hamilton:
Thanks again for your vaulable insights. I would also like to add a few remarks. My Masters research focused on predicting the probabilities of Canadian Recessions using financial and macro variables post world war 2 following the Estrella and Mishkin Methodology that used a Probit model and also used the pseudo r-squared to assess the fit between a financial variable(s) and the likelihood of a future recession on an out of sample basis.
Nevetheless, and as you note, the fit is not perfect but remarkably reliable for most post world war 2 recessions and/or slower growth with lags of course.
In addition, and in that work, I also contacted Professor Zarnowitz at the New York Conference Board in the summer of 2000 and he made some very important reamrks about spreads and their predictive ability. One very important insight he added was that:
“The predictive ability depends on whether or not the change in the spread is due to a declining long-term yield or a rising short-term yield.”
At present, we have seen a rapid imbalance in both. That is, the Federal Funds rate is up 4.25 times since June 2004 while long-term rates have dropped recently in anticipation of lower future growth in my view. Meanwhile, the University of Michigan’s November inflation expectation data is anticipating a growth rate of 4.6 percent looking forward, which really is not built into the bond market at present.
Thus, it seems to me the bond market has yet to fully anticipate what is really going on. However, once thing for certain, with a rising cost of short-term money, continued high energy prices, an overbought real estate market, and what I view as an overbought energy stock market, it seems to me that there is a great deal of financial risk in these areas at present and those macro pockets are very vulnerable given an unexpected shock to come along like a rapid drop in consumer durable goods spending. Moreover, with the big 4 auto manufactuers on the ropes at the moment, and the substituion effect taking place in the transportation sector for more fuel efficient vehicles vs. the gas guzzling SUV’s, and knowing transportation is the big driver behind energy, it seems to me that ENERGY DEMAND is also very vulnerable to upset the whole macro equation if you are heavily invested in energy at present. OPEC’s recent comment that it may ‘cut’ production in the near future should also be a very big signal that someone out there is expecting a pullback in the demand for crude and with a sell off in crude I expect a macro boost in non-energy sectors of the economy that could very well maintain reasonable real gdp growth going forward should me expectations get realized over the next 1 – 3 quarters.
If not, then the risks in the energy sector and the US economy will continue to mount and inevitablity lead to a much stronger and sharper sell off that in part has been anticipated by the change in the interest rate spread that many are talking about at present but choose to ignore for perhaps political reasons.
Finally, the data will set us all free in 2006 and I would hope that many economists still believe in the strength of lags in interest rate changes, over bought asset markets, overweighting the current information set in the market, and the accompanying optimism that ‘always’ conincides strongly with excess asset price and economic growth….

1. I don’t like the macro mixing of concepts in the same sentence. The short term funds went up because of Fed fund raises. The reason for those raises is another issue. And I hate that “they raised rates to slow the economy”. Maybe they raised rates to stop injecting money?
2. Long term yeilds fell a quarter of a percent in a month. Is that a big deal? How does it compare to typical variability (whatever causes it)?
3. And then you have 3(!) factors to explain the quarter percent drop? Which do you think accounts for most of the change? Are they independant factors and what do they mean? INflation expectation, I understand, but what exactly are term premium and especially “level of economic expectation” from a bond investor perspective? Can you connect those to something economic like beta or CAPM?

Thanks for your comments TCO. My response is as follows:
1. First, you have to consider a ‘mix’ of macroeconomic activity and asset prices as nothing is fixed and completely independent in the market. That is, asset prcies are very much a function of macro conditions and this notion is very well supported in the literature. Simply stated, monetary policy has a large impact on both currency and bond markets and equity markets within the short run, especially on the expectation side of asset pricing. Where is the proof? Please review the literature and notice the immediate impact on bond prices when rate changes are made. There are some good Federal Reserve papers on this and the NBER also has some great work. Does the fundamental economy change as fast as the press release about interest rate increases/decreases? No, but expectations about the future impact on bond prices do. In turn, also examine the relationship between increasing or decreasing interest rates and relative currency valuations. From 2001 – 2004, the US$ was out of favor and from June 2004 – present the US$ has been in favour due the short-term spread difference and higher economy growth – all current account deficit arguments aside – if you review much of the work in this area you will find some very credible arguments stating the US$ was about to take a large hit based on rigid models and it simply did not. I have been very US$ bullish since 2004 and its up about 15 percent year over year vs. Major Trading currencies. Finally, and in my view, short-term rate increases ‘do’ have an impact on stock prices once again immediately on the expectations side of the economy. Simply examine stock prices on a FOMC day and shortly thereafter and you will appreciate my view on this. I know that over longer periods the impact of rate changes on stock prices may not be as pervasive. Thus, how can you ‘not’ look at the mixing of the macroeconomy and asset pricing? Here are two great sources supporting the abvoe point of view: Chen, 1991, “Financial Investment Opportunities and the Macroeconomy”, Journal of Finance; and Chen, 1986, Roll, and Ross, “Economic Forces and the Stock Market”, Journal of Business.
2. Second, and in my view, the Fed has been increasing the Federal Funds rate to do 2 things even though I do not ever expect it to admit the first point:
i. slowly remove the excess stimulus pumped into the US economy from 2001 – 2004 when it dropped the Federal Funds rate to a late 1950s low and removing money does remove stimulus simply through the money multiplier effect and there is likely an expectational impact as well;
ii. to anticipate and prevent any potential actual and inflation ‘expectations’ from entering both the macro economy and the expectation sets of forward looking financial market participants.
3. With respect to your remark about the quarter point drop for longer term rates, I would associate that decline with the market ‘expectations’ that future growth will be lower that in turn lead to an eventual cut in short-term lending rates, which is likely why bond prices have been grinding longer yields lower recently. Personally, I am not convinced that CAPM does a great job capturing short run effects such as the immediate changes in expectations. Please see NBER’s work on CAPM and asset pricing. Charles Engle’s 1993 work is interesting.
Finally, with Fed policy changes, it is my view that very short-run effects are hard to capture with relatively fixed linear approximations to nonlinear asset prices changes that call for time varying coefficients. However, this is where I continue to view the market as providing a lot of opportunity knowing the above and I think that the growing field of behavioural finance does and will continue to help explain what CAPM and some other older asset pricing models do not in the short run and perhaps long run as well.

Kirby,
That’s an interesting post. (following your numbers)
1. First, obviously governmental and monetary policy has an effect on behavior of firms in the aggregate (so does the weather, so does war, so do technical developments).
2. My criticism of James and of fluffy, tossing words out macro writing in general, is the failure to clearly label and argue the connections. (Let’s at least have falsifiable hypotheses. Make an assertion in clear language/logic.) For instance, did the Fed raise the short term rates to slow the economy or did they do it to lower money injection and THUS slowed the economy, incidentally. But in any case, these issues are distracting from the main argument which is what drove rates. Why segue into different (debatable) paranthetical assertions that are not supports of the main argument? Your interpretation that the Fed is raising rates to lower inflation (if I boil your words down) makes much more sense.*
3. I still wonder if the change in long term rates is remarkable in terms of month to month changes or even on an intrinsic standpoint–I mean look, it’s a quarter percent! I’m glad that you nail it down to one factor vice 3 at least.
4. On CAPM, etc. My point is not so much to that specific model (although starting from the true religion before deviating is a good way to be…) Maybe I misphrase it. But what I want to hear is something that in the end can be understood in terms of incentives. There is something slippery and illogical about how macro-weenies tend to discuss things, mixing concepts and actors and waving hands vice making clear assertions.
*I do wonder a bit about your comments differentiating previous and future inflation. For instance in 2i, are you going so far as to say that the Fed is deflating the currency? It would seem much simpler just to argue 2ii. If you want to allude to 2i, would be simpler to say that they want to signal a change in BEHAVIOR rather than actually reversing effects.

Thanks TCO.
I must say that I do expect that Blogs and the availablity of global unrestricted thought will continually make each of us better and more knowledgeable.
Nevertheless, my response to your recent comments is as follows:
1. First, you have to start somewhere with a response and usually it does begin from a broad that eventually converges to a much narrower answer / solution to a problem. You are very right, the weather such as Hurriance Katrina does have an impact on the market and expectations and in fact lowered the temporary valuation of a stock pick of mine from increasing +15 percent to a +4.5 percent since my initial pick date. Accordingly, it is wise to look broad at first rather than jumping to the effect; we must look for causal factors first that requires a lot of thought and analysis. Having worked in the brokerage business years ago, I do know that many financial market participants simply want the quick and simple explanation to an often complex problem. For instance, when companies put share price targets on stocks they usually can be reduced down to a simple linear future value calculation that is extrapolated based on recent earnings trend for the most part that inevitability does not have that much of an influence on the actual outcome but it sells a lot of stock in the meantime. Commodity price forecasts are really no different as there is usually some self serving bias dependent upon who is putting them out. Accordingly, we must look macro then micro for the truth;
2. I do believe that the Fed’s aim of increasing the Federal Funds rate is to ward off potential future inflation that comes directly from too much stimulus in the economic and financial system. I wrote a review on the gold sector in late 2005 and determined that both the fundamental demand for gold has jumped considerably as has the ‘speculative’ demand for gold, or the expectations side of gold pricing has really taken off. Why? Asia in particular has been buying gold en masse due to one simple thing: a hedge against actual inflation growth that is being couched in current higher future inflation growth expectations and commodity price inflation. I took advantage of this by recommending 4 gold producers and was 4/4 on average +11 percent within 6 weeks late last year;
3. The long end of the bond market is very interesting at the moment. I do expect that long rates have dropped based on lower future growth expectations and therefore a potential cut in the Federal Funds rate down the road. The macro wild card at the moment is the price of crude that has led to higher future inflation expectations. For example, year over year, ‘actual’ core inflation growth is as follows:
PPI: +0.9%;
CPI: +1.7%
Personal Consumption Exp’s: +1.4%
GDP Deflator: +1.46 %
all are lower than the 2004 ‘actual’ data. However, the November University of Michigan Inflation Expectation data is +4.6%, or almost double 2004′ +2.8% expectation.
Thus, if crude prices remain high it is likely that longer-term rates will report higher levels, however, I am of what seems to be a very lonely view at the moment, that crude is on its way to $35ish/West Texas on or before the following 8-month horizon. OPEC’s comment about a output cut should be signaling some forward looking infomation. I would expect that lower crude prices will drop both inflation expectations and take pressure off of the Fed;
4. Incentives? In short, the market is greedy and aims to do two things: attempt to achieve exceess rates of returns; or, preserve capital and prevent excess losses. The incentive is to be able to read ahead of the data to anticipate coming changes as long as you can prevent yourself from extrapolating the immediate state, good or bad, indefinitely and in a constant manner forever in to the future, which the market loves to do. I do not view the Fed’s role to deviate from its aim of fostering ‘sustainable economic growth by achieving price stability’ that does include having some inflation growth in the economy as Japan’s example of deflation is not a fun one;
I liked your comment about deflating the US$. It would be a nice and quiet way to help correct the trade deficit. However, I do expect that through continued US political pressure on Chinese Officals, we are going to see the Yuan revalued up or floated in the not so distant future, which will help correct the trade deficit.

There’s been a lot of discussion about the yield curve lately. Some of you may be afraid to ask what a yield curve is and how it relates to interest rate spreads. For those who are, here’s a simple illustration.

When I was in grad school in the 90’s the thinking was that there is a Phillips curve in the short term, especially if inflation is not anticipated.
The Fed has 3 jobs in monetary policy: lender of last resort, preserver of the value of the currency (low to no inflation), full employment. I would guess that most at the Fed would agree that this is in order of importance. The Fed, in it’s first role will even boost money supply ahead of a banking crisis in order to avert it (as in the Y2K non-crisis).
They have told us that they know how to manage inflation, but that they are not sure if they can manage deflation. When deflation looked like a possibility and before Bush’s West Asian wars eliminated the possibilty that the US would redeem all it’s debt, the Fed seemed to be more concerned that they avoid deflation than inflation. Now that this perceived problem has ‘resolved’ itself, they are returning to their so-called neutral policy position. There was at no time any concern, except in the most general and broadest sense, about the impact on production and consumption. Anything that happened in the real economy on account of monetary policy in the last 6 years was tangential to performance of the roles as lender of last resort and responsibility for a stable currency.